How do/should cell biologists calculate power of analysis?

Often times you only see POA for clinical studies or studies involving humans. However, I'm under the impression that ANY scientist should perform POA before conducting and experiment to determine the correct sample size for an experiment. An underpowered study has the well known problem of having type II statistical errors, but I also found this interesting paper that say that paradoxically, if one finds a statistically significant finding in an underpowered study, it might actually be a type I error.

However, how do cell biologists conduct POA? The sample sizes needed that are mentioned in a POA are often huge (say 50-200 samples for an experiment designed for ANOVA w/ a power of 0.8 and moderate effect size). What am I doing wrong? Obviously it is impossible for the cell biologist to collect that many biologically independent samples, how do you calculate POA then? I know the "triplicate biological w/ triplicate technical" is quite standard, but what is so magical about 3x3? POA should be done to address proper sample size, I'm just not sure how I go about doing it relative to cell biology work.

A lot of people use the incorrect statistical tests for their work, parametric tests such as ANOVA are usually not appropriate for the types of data being generated. Ideally cell biologists would be using non-parametric tests that have a lower power, but are more appropriate to the sample sizes and data generated (e.g. ANOVA assumes normally distributed data, non-parametrics don't).